Preamble detection with multiple receive antennas

ABSTRACT

A system including a differential demodulation module, a first summing module, and a second summing module. The differential demodulation module generates differentially demodulated signals based on having differentially demodulated received signals. The first summing module generates a combined signal by adding the differentially demodulated signals, wherein the combined signal includes a plurality of symbols. The second summing module generates a plurality of sums for each of a plurality of derived preamble sequences, wherein the derived preamble sequences are derived from preamble sequences, and wherein each of the derived preamble sequences includes a plurality of derived symbols. The second summing module further generates cross-correlation values for the derived preamble sequences based on the plurality of sums, wherein one of the cross-correlation values generated for one of the derived preamble sequences is a sum of the plurality of sums generated for the one of the derived preamble sequences.

CROSS-REFERENCE TO RELATED APPLICATIONS

This present disclosure is a continuation of U.S. application Ser. No.11/820,397, filed on Jun. 19, 2007, which is a continuation of U.S.application Ser. No. 11/753,953 (now U.S. Pat. No. 7,991,077), filed onMay 25, 2007, which claims priority under 35 U.S.C. §119(3) to U.S.Provisional Application No. 60/809,733, filed on May 31, 2006, and U.S.Provisional Application No. 60/826,392, filed on Sep. 21, 2006. Thepresent disclosure is related to U.S. application Ser. No. 11/820,313(now U.S. Pat. No. 7,876,858).

FIELD

The present disclosure relates to communication systems, and moreparticularly to detecting preamble sequences in systems using orthogonalfrequency domain multiplexing (OFDM).

BACKGROUND

The background description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent it is described in thisbackground section, as well as aspects of the description which may nototherwise qualify as prior art at the time of filing, are neitherexpressly nor impliedly admitted as prior art against the presentdisclosure.

Referring now to FIG. 1, a typical communication system 10 comprises aninformation source 12, a transmitter 13, a communication channel 20, areceiver 27, and a destination 28. The transmitter 13 comprises a sourceencoder 14, a channel encoder 16, and a modulator 18. The receiver 27comprises a demodulator 22, a channel decoder 24, and a source decoder26.

The information source 12 may be an analog source such as a sensor thatoutputs information as continuous waveforms or a digital source such asa computer that outputs information in a digital form. The sourceencoder 14 converts the output of the information source 12 into asequence of binary digits (bits) called an information sequence u. Thechannel encoder 16 converts the information sequence u into a discreteencoded sequence v called a codeword. The modulator 18 transforms thecodeword into a waveform of duration T seconds that is suitable fortransmission.

The waveform output by the modulator 18 is transmitted via thecommunication channel 20. Typical examples of the communication channel20 are telephone lines, wireless communication channels, optical fibercables, etc. Noise, such as electromagnetic interference, inter-channelcrosstalk, etc., may corrupt the waveform.

The demodulator 22 receives the waveform. The demodulator 22 processeseach waveform and generates a received sequence r that is either adiscrete (quantized) or a continuous output. The channel decoder 24converts the received sequence r into a binary sequence u′ called anestimated information sequence. The source decoder 26 converts u′ intoan estimate of the output of the information source 12 and delivers theestimate to the destination 28. The estimate may be a faithfulreproduction of the output of the information source 12 when u′resembles u despite decoding errors that may be caused by the noise.

Communication systems use different modulation schemes to modulate andtransmit data. For example, a radio frequency (RF) carrier may bemodulated using techniques such as frequency modulation, phasemodulation, etc. In wireline communication systems, a transmitted signalgenerally travels along a path in a transmission line between atransmitter and a receiver. In wireless communication systems, however,a transmitted signal may travel along multiple paths. This is becausethe transmitted signal may be reflected and deflected by objects such asbuildings, towers, airplanes, cars, etc., before the transmitted signalreaches a receiver. Each path may be of different length. Thus, thereceiver may receive multiple versions of the transmitted signal. Themultiple versions may interfere with each other causing inter symbolinterference (ISI). Thus, retrieving original data from the transmittedsignal may be difficult.

To alleviate this problem, wireless communication systems often use amodulation scheme called orthogonal frequency division multiplexing(OFDM). In OFDM, a wideband carrier signal is converted into a series ofindependent narrowband sub-carrier signals that are adjacent to eachother in frequency domain. Data to be transmitted is split into multipleparallel data streams. Each data stream is modulated using asub-carrier. A channel over which the modulated data is transmittedcomprises a sum of the narrowband sub-carrier signals, which mayoverlap.

When each sub-carrier closely resembles a rectangular pulse, modulationcan be easily performed by Inverse Discrete Fourier Transform (IDFT),which can be efficiently implemented as an Inverse Fast FourierTransform (IFFT). When IFFT is used, the spacing of sub-carriers in thefrequency domain is such that when the receiver processes a receivedsignal at a particular frequency, all other signals are nearly zero atthat frequency, and ISI is avoided. This property is calledorthogonality, and hence the modulation scheme is called orthogonalfrequency division multiplexing (OFDM).

Referring now to FIGS. 2A-2C, a wireless communication system 50 maycomprise base stations BS1, BS2, and BS3 (collectively BS) and one ormore mobile stations (MS). Each BS may comprise a processor 30, a mediumaccess controller (MAC) 32, a physical layer (PHY) module 34, and anantenna 36 as shown in FIG. 2B. Similarly, each MS may comprise aprocessor 40, a medium access controller (MAC) 42, a physical layer(PHY) module 44, and an antenna 46 as shown in FIG. 2C. The PHY modules34 and 44 may comprise radio frequency (RF) transceivers (not shown)that transmit and receive data via antennas 36 and 46, respectively.Each BS and MS may transmit and receive data while the MS moves relativeto the BS.

Specifically, each BS may transmit data using orthogonal frequencydivision multiplexing access (OFDMA) system. Each BS may transmit datatypically in three segments: SEG1, SEG2, and SEG3. The MS, which movesrelative to each BS, may receive data from one or more base stationsdepending on the location of the MS relative to each BS. For example,the MS may receive data from SEG3 of BS1 and SEG2 of BS2 when the MS islocated as shown in FIG. 2A.

Relative motion between MS and BS may cause Doppler shifts in signalsreceived by the MS. This can be problematic since systems using OFDMAare inherently sensitive to carrier frequency offsets (CFO). Therefore,pilot tones are generally used for channel estimation refinement. Forexample, some of the sub-carriers may be designated as pilot tones forcorrecting residual frequency offset errors.

Additionally, the PHY module 34 of each BS typically adds a preamble toa data frame that is to be transmitted. Specifically, the PHY module 34modulates and encodes the data frame comprising the preamble at a datarate specified by the MAC 34 and transmits the data frame. When the PHYmodule 44 of the MS receives the data frame, the PHY module 44 uses thepreamble in the data frame to detect a beginning of packet transmissionand to synchronize to a transmitter clock of the BS.

According to the I.E.E.E. standard 802.16e, which is incorporated hereinby reference in its entirety, a first symbol in the data frametransmitted by the BS is a preamble symbol from a preamble sequence. Thepreamble sequence typically contains an identifier called IDcell, whichis a cell ID of the BS, and segment information. The BS selects thepreamble sequence based on the IDcell and the segment number of the BS.Each BS may select different preamble sequences. Additionally, each BSmay select preamble sequences that are distinct among the segments ofthat BS.

The BS modulates multiple sub-carriers with the selected preamblesequence. Thereafter, the BS performs IFFT, adds a cyclic prefix, andtransmits a data frame. The MS uses the cyclic prefix to perform symboltiming and fractional carrier frequency synchronization. Unless the MSknows the preamble sequence, however, the MS cannot associate itself toa particular segment of a particular BS.

SUMMARY

In general, in one aspect, this specification discloses a systemincluding a differential demodulation module, a first summing module,and a second summing module. The differential demodulation module isconfigured to generate differentially demodulated signals based onhaving differentially demodulated received signals. The first summingmodule is configured to generate a combined signal by adding thedifferentially demodulated signals, wherein the combined signal includesa plurality of symbols. The second summing module is configured togenerate a plurality of sums for each of a plurality of derived preamblesequences, in which the derived preamble sequences are derived frompreamble sequences, and each of the derived preamble sequences includesa plurality of derived symbols. One of the plurality of sums generatedfor one of the derived preamble sequences is a sum of (i) a firstportion of one of the plurality of symbols of the combined signal and(ii) a second portion of one of the derived symbols of the one of thederived preamble sequences. The second summing module is furtherconfigured to generate cross-correlation values for the derived preamblesequences based on the plurality of sums, in which one of thecross-correlation values generated for one of the derived preamblesequences is a sum of the plurality of sums generated for the one of thederived preamble sequences.

In general, in another aspect, this specification describes a methodincluding generating differentially demodulated signals bydifferentially demodulating received signals, and generating a combinedsignal by adding the differentially demodulated signals, in which thecombined signal includes a plurality of symbols. The method furtherincludes generating a plurality of sums for each of a plurality ofderived preamble sequences, in which the derived preamble sequences arederived from preamble sequences, and each of the derived preamblesequences includes a plurality of derived symbols. One of the pluralityof sums generated for one of the derived preamble sequences is a sum of(i) a first portion of one of the plurality of symbols of the combinedsignal and (ii) a second portion of one of the derived symbols of theone of the derived preamble sequences. The method further includesgenerating cross-correlation values for the derived preamble sequencesbased on the plurality of sums, wherein one of the cross-correlationvalues generated for one of the derived preamble sequences is a sum ofthe plurality of sums generated for the one of the derived preamblesequences.

In still other features, the systems and methods described above areimplemented by a computer program executed by one or more processors.The computer program can reside on a computer readable medium such asbut not limited to memory, non-volatile data storage and/or othersuitable tangible storage mediums.

Further areas of applicability of the present disclosure will becomeapparent from the detailed description provided hereinafter. It shouldbe understood that the detailed description and specific examples, whileindicating the preferred embodiment of the disclosure, are intended forpurposes of illustration only and are not intended to limit the scope ofthe disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure will become more fully understood from thedetailed description and the accompanying drawings, wherein:

FIG. 1 is a functional block diagram of an exemplary communicationsystem according to the prior art;

FIG. 2A is a schematic representation of an exemplary wirelesscommunication system comprising three base stations and a mobile stationaccording to the prior art;

FIG. 2B is a functional block diagram of an exemplary base stationutilized in the system of FIG. 2A;

FIG. 2C is a functional block diagram of an exemplary mobile stationutilized in the system of FIG. 2A;

FIG. 3 is a schematic representation of an exemplary wirelesscommunication system comprising three base stations and a mobilestation;

FIG. 4 is a table showing preamble sequences used by base stations ofFIG. 3 to transmit data;

FIG. 5A is a functional block diagram of an exemplary preamble detectionsystem according to the present disclosure;

FIG. 5B is a graph showing normalized cross-correlation between preamblesequences of FIG. 4;

FIG. 5C is a graph showing normalized cross-correlation between preamblesequences of FIG. 4 when integer carrier frequency offset is present;

FIG. 5D is a graph showing variation in channel gain relative tosub-carrier frequency in a highly frequency-selective channel;

FIG. 6A is a functional block diagram of an exemplary preamble detectionsystem according to the present disclosure;

FIG. 6B is a graph showing normalized cross-correlation between preamblesequences derived from the preamble sequences shown in FIG. 4;

FIG. 6C is a graph showing normalized cross-correlation between derivedpreamble sequences when integer carrier frequency offset is present;

FIG. 7A is a functional block diagram of an exemplary preamble detectionsystem according to the present disclosure;

FIG. 7B is a functional block diagram of an exemplary segment selectionsystem according to the present disclosure;

FIGS. 8A-8B depict a flowchart of an exemplary method for detectingpreamble sequences according to the present disclosure;

FIG. 9A is a flowchart of an exemplary method for detecting preamblesequences when sub-carriers have substantially similar channel phase;

FIG. 9B is a flowchart of an exemplary method for detecting preamblesequences when sub-carriers have an unknown differential similar channelphase;

FIG. 9C is a flowchart of an exemplary method for detecting preamblesequences when sub-carriers have substantially similar channel phase;

FIG. 10A is a functional block diagram of a vehicle control system;

FIG. 10B is a functional block diagram of a cellular phone; and

FIG. 10C is a functional block diagram of a mobile device.

DETAILED DESCRIPTION

The following description is merely exemplary in nature and is in no wayintended to limit the disclosure, its application, or uses. For purposesof clarity, the same reference numbers will be used in the drawings toidentify similar elements. As used herein, the term module, circuitand/or device refers to an Application Specific Integrated Circuit(ASIC), an electronic circuit, a processor (shared, dedicated, or group)and memory that execute one or more software or firmware programs, acombinational logic circuit, and/or other suitable components thatprovide the described functionality. As used herein, the phrase at leastone of A, B, and C should be construed to mean a logical (A or B or C),using a non-exclusive logical or. It should be understood that stepswithin a method may be executed in different order without altering theprinciples of the present disclosure.

Referring now to FIG. 3, a wireless communication system 100 maycomprise base stations BS1, BS2, and BS3 (collectively BS) and one ormore mobile stations (MS). Generally, one MS may communicate with up tothree adjacent base stations. Each BS may transmit data that ismodulated using an orthogonal frequency division multiplexing access(OFDMA) system.

Specifically, each BS may transmit data in three segments: SEG1, SEG2,and SEG3. The MS, which may move relative to each BS, may receive datafrom one or more base stations depending on the location of the MSrelative to each BS. For example, the MS may receive data from SEG3 ofBS1, SEG2 of BS2, and/or SEG1 of BS3 when the MS is located as shown.

When a receiver in the MS is turned on (i.e., when the MS is poweredup), the MS may associate with an appropriate segment of a correspondingBS depending on the location of the MS. The MS, however, can processdata in a frame transmitted by a BS only if the MS can correctly detecta preamble sequence in the frame. Specifically, the MS can perform framesynchronization and retrieval of a cell ID (IDcell) and a segment numberof the BS from the frame if the MS can detect the preamble sequence inthe frame.

Referring now to FIG. 4, OFDMA systems may use 1024 and 512 sub-carriersto modulate and transmit data. OFDMA systems using 1024 and 512sub-carriers are generally referred to as OFDMA systems having 1024 and512 FFT modes, respectively. Additionally, I.E.E.E. 802.16e supports 128FFT and 2048 FFT modes.

A total of 114 preamble sequences exist for OFDMA systems that use fastFourier transforms (FFT) to modulate 1024 and 512 sub-carriers. Eachpreamble sequence is unique. That is, each preamble sequence is distinctfrom another preamble sequence and is identified by an index number. Theindex number may be referred to as preamble sequence index. Eachpreamble sequence is 284 and 143 bits long for 1024 and 512 FFT modes,respectively.

Since one MS may typically communicate with up to three base stations,each BS modulates every third sub-carrier. That is, each BS modulatesone of every three sub-carriers. Additionally, each BS uses only one bitof the total bits in a preamble sequence when modulating every thirdsub-carrier. For example, in 1024 FFT mode, the BS may use bit numbers1, 2, 3, . . . , etc., of the 284 bits in a preamble sequence tomodulate sub-carrier numbers 1, 4, 7, . . . , etc., of the 1024sub-carriers, respectively.

Each BS may use the same set of sub-carriers. Each segment in a BS,however, uses distinct sub-carriers at least for preamble purposes. Forexample, for each BS, segment 1 (SEG1) may use sub-carriers 0, 3, 6, 9,. . . , etc.; segment 2 (SEG2) may use sub-carriers 1, 4, 7, 10, etc.;and segment 3 (SEG3) may use sub-carriers 2, 5, 8, 11, . . . , etc.

Consequently, the MS receives distinct signals from each BS. Forexample, the MS may receive signals from SEG2 of BS2 on sub-carriers 1,4, 7, 10, . . . , etc., from SEG1 of BS3 on sub-carriers 0, 3, 6, 9, . .. , etc., and from SEG 3 of BS1 on sub-carriers 2, 5, 8, 11, . . . ,etc. Thus, the signals received by the MS may not interfere with eachother since their sub-carriers are distinct.

A set of sub-carriers for segment n may be mathematically expressed asfollows.PreambleCarrierSet_(n) =n+3kwhere 0≦k≦283 for 1024 FFT mode and 0≦k≦142 for 512 FFT mode.Additionally, there may be 86 guard sub-carriers on the left and rightends of the spectrum in 1024 FFT mode. In the 512 FFT mode, there may be42 guard sub-carriers on the left end and 41 guard sub-carriers on theright end.

Typically, when the receiver in the MS is turned on, the MS initiallyperforms symbol timing and carrier frequency synchronization before theMS can detect a preamble sequence. The MS may perform these tasks usinga cyclic prefix in the data frame. Thereafter, the MS determines whethera first symbol in the frame is a preamble symbol. If the first symbol isa preamble symbol, then the MS determines which preamble sequence ispresent in the frame. Once the MS determines the preamble sequence, theMS can associate with a corresponding segment of an appropriate BS.

Symbols in preamble sequences (i.e., preamble symbols) typically havehigher energy than data symbols. For example, the energy of the preamblesymbols is typically 8/3 times (i.e., 4.26 dB higher than) the energy ofdata symbols. This is useful in distinguishing preamble symbols fromdata symbols.

Additionally, the preamble sequences are almost orthogonal. That is, across-correlation between any two preamble sequences is very small. Forexample, the cross-correlation is typically less than 0.2. This isuseful in distinguishing individual preamble sequences from one another.As shown in the table in FIG. 4, if the MS detects a preamble sequencehaving an index 0, then the MS associates with segment 0 of BS havingcell ID 0, and so on.

Base stations and mobile stations may be configured to operate in WiMAXwireless networks. WiMAX is a standards-based technology enablingwireless broadband access as an alternative to wired broadband likecable and DSL. WiMAX provides fixed, nomadic, portable, and mobilewireless connectivity without the need for a direct line-of-sight with abase station. WiMAX technology may be incorporated in portableelectronic devices such as notebook computers, personal digitalassistants (PDAs), etc. The WiMAX standards enumerated in “Stage 2Verification And Validation Readiness Draft,” Release 1, dated Aug. 8,2006 and “Stage 3 Verification And Validation Readiness Draft,” Release1, dated Aug. 8, 2006 are incorporated herein by reference in theirentirety.

Mobile WiMAX supports a full range of smart antenna technologiesincluding beamforming, spatial multiplexing, etc., to enhance systemperformance. Mobile WiMAX supports adaptive switching between theseoptions to maximize the benefit of smart antenna technologies underdifferent channel conditions. Smart antenna technologies typicallyinvolve complex vector and matrix operations on signals due to multipleantennas. Typically, base stations may have at least two transmitantennas but may transmit preamble symbols via only one transmitantenna. Mobile stations may have at least two receive antennas and mayreceive signals via more than one receive antenna.

Referring now to FIGS. 5A-5D, a system 150 for detecting preamblesequences in a mobile station (MS) having at least two receive antennasmay be implemented in a physical layer (PHY) module 152 of the MS. Thesystem 150 comprises a correlation module 154 and a control module 156.The correlation module 154 receives input signals transmitted by a basestation (BS).

The correlation module 154 receives the input signals via the receiveantennas. The input signals received by the receive antennas may bemathematically expressed as follows.

$\begin{matrix}{{Y_{1}\lbrack k\rbrack} = {{{H_{1}\lbrack k\rbrack}{X_{i}\lbrack k\rbrack}} + {Z_{1}\lbrack k\rbrack}}} \\\vdots \\{{Y_{R}\lbrack k\rbrack} = {{{H_{R}\lbrack k\rbrack}{X_{i}\lbrack k\rbrack}} + {Z_{R}\lbrack k\rbrack}}}\end{matrix}$where k is sub-carrier index, i is preamble sequence index, R is totalnumber of receive antennas, and X_(i)[k] is transmit signalcorresponding to preamble sequence index i at sub-carrier k.Additionally, Y_(r)[k], H_(r)[k], and Z_(r)[k] are received signal(i.e., input signal), channel gain, and noise for a receive antenna r atsub-carrier k, respectively. That is, each of R receive antennasreceives a separate input signal having separate channel and noise.

When a preamble bit (i.e., a preamble symbol) in a preamble sequence is0, the corresponding transmit signal X_(i)[k] is 1. When a preamble bitin a preamble sequence is 1, the corresponding transmit signal X_(i)[k]is −1. That is, when a preamble bit in a preamble sequence is 1, thechannel phase of the sub-carrier in the transmit signal X_(i)[k] isshifted by π relative to the channel phase of the sub-carrier when apreamble bit in a preamble sequence is 0.

The system 150 detects a preamble sequence in the input signals receivedby the receive antennas as follows. The correlation module 154correlates the input signals received by the receive antennas withpreamble sequences and generates correlation values. The preamblesequences may be stored in memory in the correlation module 154 or thecontrol module 156. Based on the correlation values, the control module156 initially determines whether a first symbol in the input signals isa preamble symbol or a data symbol. If the first symbol is a preamblesymbol, then the control module 156 determines an index i of thepreamble sequence. Based on the index i of the preamble sequencedetected, the control module 156 determines which segment transmittedthe preamble sequence. Accordingly, the MS associates with that segment.

When all k sub-carriers have a common channel gain H_(r) (i.e., whenH_(r)[k] is independent of k) and the same random channel phase, the ksub-carriers are referred to as “almost flat frequency channels.” Foralmost flat frequency channels, the input signals may be mathematicallyexpressed as follows.

$\underset{\sum\limits_{k \in P_{s}}\;{{X_{0}{\lbrack k\rbrack}}}^{2}}{{Y_{r}\lbrack k\rbrack} = {{{{H_{r}\lbrack k\rbrack}{X_{i}\lbrack k\rbrack}} + {Z_{r}\lbrack k\rbrack}} \approx {{H_{r}{X_{i}\lbrack k\rbrack}} + {Z_{r}\lbrack k\rbrack}}}}$

A cross-correlation between different preamble sequences is given by thefollowing formula.

${\max\limits_{i,{j \neq i}}\{ \frac{{\sum\limits_{k \in P_{s{(i)}}}{{X_{i}\lbrack k\rbrack}{X_{j}^{*}\lbrack k\rbrack}}}}{\sum\limits_{k \in P_{s{(i)}}}{{X_{i}\lbrack k\rbrack}}^{2}} \}} \approx {0.1620\mspace{14mu}{for}\mspace{14mu} 1024\mspace{14mu}{FFT}}$where Ps=set of pilot sub-carriers for segment s except left most pilotsub-carrier, and s(i)=segment number for a preamble sequence index i.FIG. 5B shows cross-correlation values normalized by for 1024 FFT mode.

Since the cross-correlation between different preamble sequences issmall, the correlation module 154 correlates the input signal receivedby each of R receive antennas with all j preamble sequences as follows.

$C_{j,r} = {\sum\limits_{k \in P_{s{(j)}}}{{Y_{r}\lbrack k\rbrack}{X_{j}^{*}\lbrack k\rbrack}}}$Specifically, the correlation module 154 correlates all modulatedsub-carriers in each input signal with each of j preamble sequences.Thus, the correlation module 154 generates j correlation values perreceive antenna. For example, in 1024 FFT mode, the correlation module154 correlates each input signal with each of the 114 preamble sequencesand generates 114 correlation values per receive antenna.

The control module 156 adds magnitudes of correlation values of eachinput signal that correspond to the same preamble sequence, generates jcorrelation sums, and selects a largest correlation sum from the jcorrelation sums. This is mathematically expressed as follows.

$\hat{i} = {\underset{j}{\arg\;\max}\{ {\sum\limits_{r = 1}^{R}{C_{j,r}}} \}}$Specifically, the correlation module 154 may generate correlation valuesC₁₁, C₂₁, . . . , C_(j1) by correlating j preamble sequences with theinput signal received by receive antenna 1, C₁₂, C₂₂, . . . , C_(j2) bycorrelating j preamble sequences with the input signal received byreceive antenna 2, etc. The control module 156 adds magnitudes of C₁₁and C₁₂, C₂₁ and C₂₂, . . . , C_(j1) and C_(j2) and generatescorrelation sums C₁, C₂, . . . , C_(j) respectively.

The control module 156 compares the largest correlation sum to apredetermined threshold. The predetermined threshold is a function ofsignal strength of the input signals. If the largest correlation sum isgreater than or equal to the predetermined threshold, the control module156 determines that a preamble sequence is detected in the inputsignals.

Thereafter, the control module 156 determines which segment transmittedthe preamble sequence that the control module 156 detected in the inputsignal. The input signals may be transmitted by up to three differentsegments of three different base stations. The control module 156determines which segment transmitted the preamble sequence implicitlywhen the control module 156 detects the preamble sequence. This isbecause each preamble sequence is unique as identified by a uniquepreamble sequence index number, and each segment transmits a uniquepreamble sequence using distinct sub-carriers.

Thus, when the control module 156 detects the preamble sequence byselecting the largest correlation sum, the control module 156 implicitlyselects the segment having maximum channel gain. Thus, when the controlmodule 156 detects the preamble sequence, the control module 156implicitly detects which segment transmitted the preamble sequence.

Occasionally, the input signals may comprise a carrier frequency offset(CFO). The CFO may be fractional or integer. The CFO in the inputsignals received by the receive antennas may be approximately the same.In that case, the input signals comprising a fractional CFO p may bemathematically expressed as follows.Y _(r) [k]=C(ε,0)H _(r) [k]X _(i) [k]+I _(r)(ε,k)+Z _(r) [k]where ε=ΔfNT represents normalized CFO.

The fractional CFO introduces Inter-carrier interference (ICI) as givenby the following equation.

${I_{r}( {ɛ,k} )} = {\sum\limits_{p = 1}^{N - 1}{{C( {ɛ,p} )}{H_{r}\lbrack ( ( {k - p} ) )_{N} \rbrack}{X_{i}\lbrack ( ( {k - p} ) )_{N} \rbrack}}}$where N equals total number of sub-carriers (e.g., N=1024 in 1024 FFTmode), and

${C( {ɛ,p} )} = {\frac{\sin( {\pi( {ɛ - p} )} )}{N\;{\sin( {{\pi( {ɛ - p} )}/N} )}}{\mathbb{e}}^{{{j\pi}{({ɛ - p})}}{({l - {1/N}})}}}$

Additionally, the fractional CFO decreases signal to noise ratio

(SNR) of the input signals. This is mathematically expressed as follows.

${E\lbrack {{SNR}_{r}( {ɛ,k} )} \rbrack} \approx \frac{{{C( {ɛ,0} )}}^{2}{SNR}_{r,0}}{{( {1 - {{C( {ɛ,0} )}}^{2}} ){SNR}_{r,0}} + 1}$

where SNR_(r,0) represents average SNR of receive antenna r in absenceof CFO. SNR decreases as CFO increases.

Since fractional CFO introduces ICI and attenuates the input signals,the fractional CFO adversely affects preamble sequence detection insystem 150. The fractional CFO, however, does not affect the preamblesequence detection significantly. This is because the fractional CFOadds a phase error that is common to all sub-carriers and all receiveantennas, which does not change the frequency selectivity of thechannels.

On the other hand, when the CFO is an integer l, a phase error θintroduced by the integer CFO may be common to all k sub-carriers.Additionally, the integer CFO may be similar in the input signalsreceived by each receive antenna. In that case, the input signalscomprising the integer CFO l may be mathematically expressed as follows.Y _(r) [k]=e ^(jθ) H _(r)[((k−l))_(N) ]X _(i)[((k−l))_(N) ]+Z_(r)[((k−l))_(N)]

Specifically, the integer CFO causes a cyclic shift of the input signalsin the frequency domain. In other words, the integer CFO rotates theinput signals in the frequency domain. Accordingly, the correlationmodule 154 correlates preamble sequences with shifted versions of inputsignals as given by the following equation.

$C_{j,r,m} = {\sum\limits_{k \in P_{s{(j)}}}{{Y_{r}\lbrack ( ( {k - m} ) )_{N} \rbrack}{X_{j}^{*}\lbrack k\rbrack}}}$

The control module 156 detects a preamble sequence by selecting amaximum correlation value according to the following equation.

$( {\hat{i},\hat{l}} ) = {\underset{({j,m})}{\arg\;\max}\{ {\sum\limits_{r = 1}^{R}{C_{j,r,m}}} \}}$Simultaneously, the control module 156 also estimates the integer CFOl^. FIG. 5C shows maximum correlation values normalized by

$\sum\limits_{k \in P_{s{(0)}}}{{{X_{0}\lbrack k\rbrack}}^{2}.}$

Occasionally, the channel of each receive antenna may not be almostfrequency flat. That is, the sub-carriers in a channel may not have acommon channel gain. In other words, H_(r)[k] may not be independent ofk. In that case, the channel gain may vary with frequency ofsub-carriers as shown in FIG. 5D. Such a channel is called highlyfrequency selective channel. In a highly frequency selective channel,the variation in channel gain may significantly change the channel phaseof sub-carriers and distort the correlation between transmitted andexpected preamble sequences. Consequently, the system 150 may notreliably detect correct preamble sequences by correlating all of thesub-carriers in input signals with the preamble sequences.

However, the system 150 can estimate a preamble sequence index bypartitioning channels into bands, wherein the channels may be relativelyfrequency flat, and then correlating on a per-band basis. Specifically,for each signal received by the receive antennas, the control module 156partitions the total number of sub-carriers into a predetermined numberof bands. If N denotes total number of sub-carriers in a channel, thecontrol module 156 divides the channel into L bands, each comprising NILconsecutive sub-carriers as shown in FIG. 5D. For example, in 1024 FFTmode, the control module 156 may divide the 1024 sub-carriers into 16bands, each comprising 64 successive sub-carriers. Thus, band 1 mayinclude sub-carriers 1-64, band 2 may include sub-carriers 65-128, . . ., and band 16 may include sub-carriers 961-1024.

Although the channel gain may vary across the bands, the channel gainmay not vary significantly among the sub-carriers within individualbands. The correlation module 154 performs correlation on a per-bandbasis for each receive antenna. That is, the correlation module 154correlates input signals received by the receive antennas with all thepreamble sequences on a per-band basis.

Specifically, the correlation module 154 correlates symbols in a band ofan input signal received by a first antenna with corresponding symbolsin a preamble sequence, and generates correlation values for the band,which may be called intra-band correlation values. The control module156 adds the intra-band correlation values to generate a sum andgenerates a magnitude of the sum, which may be called a band correlationvalue.

Thus for a first preamble sequence, the control module 156 generates Lband correlation values. The control module 156 adds the L bandcorrelation values to generate a correlation value C₁₁ for the firstpreamble sequence and the input signal received by the first receiveantenna. The correlation module 154 similarly correlates all j preamblesequences with the input signal received by the first receive antenna,and the control module 156 generates j correlation values C₁₁, C₂₁, . .. , C_(j1).

Correlation values C₁₂, C₂₂, . . . , C_(j2) are similarly generated bycorrelating j preamble sequences with the input signal received byantenna 2, etc. The control module 156 adds magnitudes of C₁₁ and C₁₂,C₂₁ and C₂₂, . . . , C_(j1) and C_(j2) and generates correlation sumsC₁, C₂, . . . , C_(j), respectively.

The control module 156 selects a largest of the correlation sums andcompares the largest correlation sum to a predetermined threshold, whichis a function of signal strength of the input signals. If the largestcorrelation sum is greater than or equal to the predetermined threshold,the control module 156 determines that a preamble sequence is detectedin the input signals. The control module 156 implicitly determines whichsegment transmitted the input signals based on the detected preamblesequence. The effect of variation in channel gain on the channel phaseof sub-carriers and the consequent distortion in correlation isminimized by correlating on a per-band basis and by generatingcorrelation values based on band correlation values, which aremagnitudes (i.e., absolute values).

Referring now to FIGS. 6A-6C, a system 160 for detecting preamblesequences in a mobile station (MS) having at least two receive antennasmay be implemented in a physical layer (PHY) module 162 of the MS. Thesystem 160 comprises a differential demodulation module 164, a summingmodule 165, a correlation module 166, and a control module 168.

The differential demodulation module 164 receives input signalstransmitted by a base station (BS). The differential demodulation module164 receives the input signals via the receive antennas. The inputsignals received by the receive antennas may be mathematically expressedas follows.

$\begin{matrix}{{Y_{1}\lbrack k\rbrack} = {{{H_{1}\lbrack k\rbrack}{X_{i}\lbrack k\rbrack}} + {Z_{1}\lbrack k\rbrack}}} \\\vdots \\{{Y_{R}\lbrack k\rbrack} = {{{H_{R}\lbrack k\rbrack}{X_{i}\lbrack k\rbrack}} + {Z_{R}\lbrack k\rbrack}}}\end{matrix}$where k is sub-carrier index, i is preamble sequence index, R is numberof receive antennas, and X_(i)[k] is transmit signal corresponding topreamble sequence index i at sub-carrier k. Additionally, Y_(r)[k],H_(r)[k], and Z_(r)[k] are received signal (i.e., input signal), channelgain, and noise for a receive antenna r at sub-carrier k, respectively.That is, each of R receive antennas receives a separate input signalhaving separate channel and noise.

Adjacent modulated sub-carriers (i.e., sub-carriers 1, 4, 7, etc.) mayhave similar channel phase or an unknown differential channel phase thatis common to all k sub-carriers. The unknown differential channel phasemay be caused by presence of a symbol timing offset, which in turn maybe caused by improper symbol timing synchronization. When adjacentmodulated sub-carriers have similar channel phase, the channel phasedifference between adjacent modulated sub-carriers is nearly zero.

On the other hand, when adjacent modulated sub-carriers have an unknowndifferential channel phase that is common to all k sub-carriers, thechannel phase difference between adjacent modulated sub-carriers may benon-zero. When adjacent modulated sub-carriers have similar channelphase or unknown differential channel phase common to all sub-carriers,the sub-carriers are generally referred to as “moderately frequencyselective channels.”

The differential demodulation module 164 performs a differentialdemodulation operation on each of the input signals and generatesdifferentially demodulated signals. Specifically, the differentialdemodulation module 164 multiplies a modulated sub-carrier in an inputsignal by a complex conjugate of an adjacent modulated sub-carrierlocated three sub-carriers apart. This operation is called differentialdemodulation operation.

When the adjacent modulated sub-carriers have similar channel phase, thedifferentially demodulated signals can be mathematically expressed asfollows.M _(r) [k]=Y _(r) *[k−3]Y _(r) [k]=H _(r) [k]H _(r) *[k−3]D _(i)[k]+{tilde over (Z)} _(r) [k]≈|H _(r) [k]H _(r) *[k−3]|D _(i) [k]+{tildeover (Z)} _(r) [k]where Y*[k−3] denotes a complex conjugate of a modulated sub-carrierthat is three sub-carriers apart from the modulated sub-carrier Y[k].The complex conjugate is indicated by asterisk or “*”.

Since the adjacent modulated sub-carriers have similar channel phase,the channel phase difference between the adjacent modulated sub-carriersis nearly zero. That is,∠(H[k]H*[k−3])≈0

The summing module 165 sums the differentially demodulated signals andgenerates a combined differentially demodulated signal as follows.

${M\lbrack k\rbrack} = {{\sum\limits_{r = 1}^{R}{M_{r}\lbrack k\rbrack}} \approx {{( {\sum\limits_{r = 1}^{R}{{{H_{r}\lbrack k\rbrack}{H_{r}^{*}\lbrack {k - 3} \rbrack}}}} ){D_{i}\lbrack k\rbrack}} + {\sum\limits_{r = 1}^{R}{{\overset{\sim}{Z}}_{r}\lbrack k\rbrack}}}}$

The correlation module 166 or the control module 168 stores XOR'edversions of preamble sequences in memory. XOR'ed versions of preamblesequences may also be referred to as derived preamble sequences. AnXOR'ed or derived preamble sequence is generated by XORing adjacent bitsin the preamble sequence.

For example, if one of the 114 preamble sequences in 1024 FFT modeincludes bits B1, B2, B3, . . . , B284, then an XOR'ed version of thatpreamble sequence includes bits X1, X2, X3, . . . , X284, whereX1=B1{circle around (+)}B2, X2=B2{circle around (+)}B3, etc. The derivedpreamble sequences may be mathematically expressed as follows.D _(i) [k]=X _(i) [k]X _(i) *[k−3]where the asterisk (i.e.,“*”) denotes a complex conjugate. Actuallyperforming complex conjugate operations to generate complex conjugates,however, is unnecessary since complex conjugates of 1 and −1 are 1 and−1, respectively. That is, 1*=1, and (−1)*=−1.

A cross-correlation between the derived preamble sequences is given bythe following formula.

${\max\limits_{i,{j \neq i}}\{ \frac{\sum\limits_{k \in P_{s{(i)}}}{{D_{i}\lbrack k\rbrack}{D_{j}^{*}\lbrack k\rbrack}}}{\sum\limits_{k \in P_{s{(i)}}}{{D_{i}\lbrack k\rbrack}}^{2}} \}} \approx {0.1731\mspace{14mu}{for}\mspace{14mu} 1024\mspace{20mu}{FFT}}$FIG. 6B shows cross-correlation values normalized by for 1024 FFT

$\sum\limits_{k \in P_{s{(0)}}}{{D_{0}\lbrack k\rbrack}}^{2}$mode.

Since the cross-correlation between the derived preamble sequences issmall, the correlation module 166 correlates the combined differentiallydemodulated signal with the derived preamble sequences as follows.

$\mspace{20mu}{C_{j} = {\sum\limits_{k \in P_{s{(j)}}}{{M\lbrack k\rbrack}{D_{j}^{*}\lbrack k\rbrack}}}}$

The correlation module 166 correlates all k sub-carriers in the combineddifferentially demodulated signal with each of j derived preamblesequences and generates j correlation values. For example, in the 1024FFT mode, the correlation module 166 correlates all k sub-carriers with114 derived preamble sequences and generates 114 correlation values.Since the values of D_(j)[k] (reference to complex conjugate by “*”omitted) are either 1 or −1, effectively M[k]D_(j)[k]=±M[k].

The correlation values are complex numbers, which have real andimaginary parts. The imaginary parts of the correlation values representnoise in the input signals. The control module 168 disregards theimaginary parts since:∠(H[k]H*[k−3])≈0

The control module 168 selects a correlation value having a largest realpart. This is mathematically expressed as follows.

$\hat{i} = {\underset{j}{\arg\mspace{11mu}\max}\{ {{Re}\{ C_{j} \}} \}}$The control module 168 compares the largest real part to a predeterminedthreshold. The predetermined threshold is a function of signal strengthof the input signal. If the largest real part is greater than or equalto the predetermined threshold, the control module 168 determines that apreamble sequence is detected in the input signals. As in system 150,the control module 168 implicitly determines which segment transmittedthe preamble sequence when the control module 168 detects the preamblesequence.

On the other hand, when the adjacent modulated sub-carriers have anunknown differential channel phase θ that is common to all ksub-carriers in the input signals, the differentially demodulatedsignals generated by the differential demodulation module 164 are givenby the following equation.M _(r) [k]H _(r) [k]H _(r) *[k−3]D _(i) [k]+{tilde over (Z)} _(r) [k]≈e^(jθ) |H _(r) [k]H _(r) *[k−3]|D _(i) [k]+{tilde over (Z)} _(r) [k]where ∠(H[k]H*[k−3])≈θ is not zero.

The summing module 165 sums the differentially demodulated signals andgenerates a combined differentially demodulated signal as follows.

${M\lbrack k\rbrack} = {{\sum\limits_{r = 1}^{R}{M_{r}\lbrack k\rbrack}} \approx {{{{\mathbb{e}}^{j\;\theta}( {\sum\limits_{r = 1}^{R}{{{H_{r}\lbrack k\rbrack}{H_{r}^{*}\lbrack {k - 3} \rbrack}}}} )}{D_{i}\lbrack k\rbrack}} + {\sum\limits_{r = 1}^{R}{{\overset{\sim}{Z}}_{r}\lbrack k\rbrack}}}}$

Since the cross-correlation between the derived preamble sequences issmall, the correlation module 166 correlates the combined differentiallydemodulated signal with the derived preamble sequences and generatescorrelation values similar to when the adjacent modulated sub-carriershave similar channel phase. However, because ∠(H[k]H*[k−3])≈θ is notzero, the control module 168 calculates magnitude of the largestcorrelation value instead of selecting real part of the largestcorrelation value. That is, the control module 168 does not disregardthe imaginary part of the largest correlation value. This ismathematically expressed as follows.

$\hat{i} = {\underset{j}{\arg\;\max}\{ {C_{j}} \}}$

The control module 168 compares the magnitude of the largest correlationvalue to a predetermined threshold. The predetermined threshold is afunction of signal strength of the input signal. If the magnitude of thelargest correlation value is greater than or equal to the predeterminedthreshold, the control module 168 determines that a preamble sequence isdetected in the input signals. As in system 150, the control module 168implicitly determines which segment transmitted the preamble sequencewhen detecting the preamble sequence.

As in system 150, the preamble sequence detection in system 160 is notaffected by a fractional CFO present in the input signals. When aninteger CFO is present in the input signals, the differentialdemodulation module 164 differentially demodulates the input signalshaving the integer CFO. The summing module 165 sums the differentiallydemodulated signals and generates a combined differentially demodulatedsignal having the integer CFO.

The correlation module 166 correlates derived preamble sequences withthe combined differentially demodulated signal having the integer CFO,and the control module 168 performs preamble detection according to thechannel phase of adjacent modulated sub-carriers. That is, the controlmodule 168 elects between real part and magnitude of the largestcorrelation value depending on whether the adjacent modulatedsub-carriers have substantially the same channel phase or common unknowndifferential channel phase. FIG. 6C shows maximum correlation valuesnormalized by

$\sum\limits_{k \in P_{s{(0)}}}{{{D_{0}\lbrack k\rbrack}}^{2}.}$

Occasionally, the input signals may have a small symbol timing offsetdue to improper symbol timing synchronization, which is performed whenthe MS is powered up. The symbol timing offset may cause inter-symbolinterference (ISI). Additionally, the symbol timing offset may cause aninter-carrier interference (ICI). The input signals having a symboltiming offset can be mathematically expressed as follows.

${Y_{r}\lbrack k\rbrack} = {{{\exp( \frac{j\; 2\;\pi\;\tau\; k}{N} )}{H_{r}\lbrack k\rbrack}{X_{i}\lbrack k\rbrack}} + {I_{r}( {\tau,k} )} + {Z_{r}\lbrack k\rbrack}}$where τ represents symbol timing offset and I_(r)(τ,k) represents 151and ICI.

Specifically, the symbol timing offset introduces an extra phase offsetamong the sub-carriers. The phase offset may increase linearly as thesub-carrier index k increases. In that case, system 160 may performbetter than system 150. Additionally, the extra phase offset introducedby the symbol timing offset appears in the differentially demodulatedsignals generated by the differential demodulation module 164 and thecombined differentially demodulated signal generated by the summingmodule 165. Therefore, the system 160 using the largest magnitude of thecorrelation value to detect a preamble sequence may perform better thanthe system 160 utilizing the largest real part of the correlation valueto detect the preamble sequence.

The differentially demodulated signals with the extra phase offset aremathematically expressed as follows.

${M_{r}\lbrack k\rbrack} = {{{\exp( \frac{j\; 6\;\pi\;\tau}{N} )}{H_{r}\lbrack k\rbrack}{H_{r}^{*}\lbrack {k - 3} \rbrack}{D_{i}\lbrack k\rbrack}} + {Z_{r}^{\prime}\lbrack k\rbrack}}$If the linearly increasing phase offset is too large, the control module168 calculates the magnitude of the largest correlation value instead ofselecting a largest real part of a correlation value.

In the system 160 utilizing magnitude of the largest correlation valueto detect a preamble sequence, the control module 168 simultaneouslyestimates symbol timing offset as follows. After calculating themagnitude of the largest correlation value, the control module 168measures a phase of the correlation value having the largest magnitude.The control module 168 calculates symbol timing offset by multiplyingthe phase of the correlation value having the largest magnitude by aratio of N to 3*2π. Mathematically, this may be expressed as follows.

$C_{j} = {\sum\limits_{k \in P_{s{(j)}}}{{M\lbrack k\rbrack}{D_{j}^{*}\lbrack k\rbrack}}}$$\hat{i} = {\underset{j}{\arg\mspace{11mu}\max}\{ {C_{j}} \}}$$\hat{\tau} = {\frac{N}{6\pi}\angle\; C_{\hat{i}}}$where ∠C_(ĩ) is the phase angle of the correlation value having thelargest magnitude, and N is total number of sub-carriers in an FFT mode(e.g., N=1024 in 1024 FFT mode). Additionally, multiplier 3 is used tomultiply 2π since every third sub-carrier is modulated. Thus, themultiplier may be P when every P^(th) sub-carrier is modulated, where Pis an integer greater than or equal to 1.

Referring now to FIGS. 7A-7C, a system 180 for detecting preamblesequences in a mobile station (MS) having at least two receive antennasmay be implemented in a physical layer (PHY) module 182 of the MS. Thesystem 180 comprises a differential demodulation module 164, a summingmodule 165, a state detection module 185, a modulo-2 summing module 186,and a control module 188 as shown in FIG. 7A.

The differential demodulation module 164 receives input signalstransmitted by a base station (BS). The differential demodulation module164 receives the input signals received via at least two receiveantennas. The input signals may be mathematically expressed as follows.

$\begin{matrix}{{Y_{1}\lbrack k\rbrack} = {{{H_{1}\lbrack k\rbrack}{X_{i}\lbrack k\rbrack}} + {Z_{1}\lbrack k\rbrack}}} \\\vdots \\{{Y_{R}\lbrack k\rbrack} = {{{H_{R}\lbrack k\rbrack}{X_{i}\lbrack k\rbrack}} + {Z_{R}\lbrack k\rbrack}}}\end{matrix}$where k is sub-carrier index, i is preamble sequence index, R is numberof receive antennas, and X_(i)[k] is transmit signal corresponding topreamble sequence index i at sub-carrier k. Additionally, Y_(r)[k],K[k], and Z_(r)[k] are received signal (i.e., input signal), channelgain, and noise for a receive antenna r at sub-carrier k, respectively.That is, each of R receive antennas receives a separate input signalhaving separate channel and noise.

The differential demodulation module 164 performs a differentialdemodulation operation on the input signals and generates differentiallydemodulated signals. Specifically, the differential demodulation module164 multiplies a modulated sub-carrier in an input signal by a complexconjugate of an adjacent modulated sub-carrier located threesub-carriers apart.

When the adjacent modulated sub-carriers have similar channel phase(i.e., when ∠(H[k]H*[k−3])≈0), the differentially demodulated signalscan be mathematically expressed as follows.M _(r) [k]=Y _(r) *[k−3]Y _(r) [k]=H _(r) [k]H _(r) *[k−3]D _(i)[k]+{tilde over (Z)} _(r) [k]≈|H _(r) [k]H _(r) *[k−3]|D _(i) [k]+{tildeover (Z)} _(r) [k]where Y*[k−3] denotes a complex conjugate of a modulated sub-carrierthat is three sub-carriers apart from the modulated sub-carrier Y[k].The complex conjugate is indicated by asterisk or “*”. Additionally,XOR'ed versions of preamble sequences, called derived preamblesequences, are expressed by the following equation.D _(i) [k]=X _(i) [k]X _(i) *[k−3]The derived preamble sequences have a very low cross-correlation (e.g.,0.1731 for 1024 FFT) and may be stored in the control module 188.

For moderately frequency selective channels with high signal-to-noiseratio (SNR),{tilde over (Z)}[k]<<|H[k]H*[k−3]|D _(i) [k]Thus, the differentially demodulated signals can be represented by thefollowing equation.M _(r) [k]=H _(r) [k]H _(r) *[k−3]D _(i) [k]+{tilde over (Z)} _(r)[k]≈|H _(r) [k]H _(r) *[k−3]|D _(i) [k]

The summing module 165 sums the differentially demodulated signals andgenerates a combined differentially demodulated signal as follows.

${M\lbrack k\rbrack} = {{\sum\limits_{r = 1}^{R}{M_{r}\lbrack k\rbrack}} \approx {( {\sum\limits_{r = 1}^{R}{{{H_{r}\lbrack k\rbrack}{H_{r}^{*}\lbrack {k - 3} \rbrack}}}} ){D_{i}\lbrack k\rbrack}}}$

The sign of the real part of M[k] is the same as the sign of D_(i)[k] inabsence of noise and when ∠(H[k]H*[k−3])≈0. That is, when D_(i)[k]=1,M[k] is positive or +1, and when D_(i)[k]=0, M[k] is negative or −1.This may be mathematically expressed as follows.u(Re{M[k]})=u(Re{D _(i) [k]})where u represents the sign and Re{M[k]} and Re{D_(i)[k]} represent realparts of M[k] and D_(i)[k], respectively. Thus,

${u(x)} = \{ \begin{matrix}1 & {{{for}\mspace{14mu} x} \geq 0} \\0 & {{{for}\mspace{14mu} x} < 0}\end{matrix} $That is, positive values of real part (e.g., x=+1) represent binary 1s,and negative values of real part (e.g., x=−1) represent binary 0s.Hereinafter, the word “sign” may be used interchangeably with (i.e.,synonymously as) “state” and/or “polarity.”

Signs or states of M[k] and D_(i)[k] may be used to simplifyimplementation of preamble detection as follows. Instead of performing acomplex operation of calculating correlation values between M[k] andD_(i)[k], a preamble sequence may be detected by performing XORoperations on (i.e., modulo 2 sums of) signs or states of real parts ofM[k] and D_(i)[k]. The XOR operations generate values that areequivalent to correlation values generated by performing correlation ofM[k] and D_(i)[k] using a correlation module.

Since XOR operations are simpler to implement than implementingcorrelation operations, the XOR operations will be hereinafter referredto as low-complexity cross-correlation. Consequently, values generatedby the XOR operations will be hereinafter referred to as low-complexitycross-correlation values or cross-correlation values.

The state detection module 185 detects the states or signs of symbols inM[k]. The modulo-2 summing module 186 generates the cross-correlationvalues for each preamble sequence as follows.

${\overset{\sim}{C}}_{j} = {\sum\limits_{k \in P_{s{(j)}}}{{u( {{Re}\{ {M\lbrack k\rbrack} \}} )} \oplus ( {1 - {u( {D_{j}\lbrack k\rbrack} )}} )}}$where Ps=set of pilot sub-carriers for segment s except left most pilotsub-carrier, and s(j)=segment number for a preamble sequence index j.u(Re{M[k]}) are the signs or states of the real parts of symbols inM[k], and u(D_(j)[k]) are the signs or states of the derived preamblesequences. Since the states of M[k] and D_(j)[k] are identical, the XORof states of M[k] and D_(j)[k] would be zero. Therefore, instead ofusing states of (D_(j)[k]), the modulo-2 summing module 186 uses states(1−u(D_(j)[k])), which are opposite of states of (D_(j)[k]). That is,(1−u(D_(j)[k])) is essentially the same as inverted u(D_(j)[k]).

For example, if sequence D_(j)[k] is 10110, then (1−u(D_(j)[k])) is01001. Thus, if received sequence in M[k] is the same as the transmittedsequence, the value of the sum C_(j) ^(˜) (i.e., the cross-correlationvalue) would be 5. On the other hand, if the received sequence isdifferent from 10110, the value of the sum C_(j) ^(˜) would be less than5. Stated generally, the cross-correlation value will be largest when areceived sequence in the differentially demodulated signal M[k] matchesone of differentially demodulated preamble sequences D_(j)[k].

For simplicity, (1−u(D_(j)[k])) may be hereinafter referred to aspredetermined states of preamble sequences. The control module 188 maystore the predetermined states (1−u(D_(j)[k])) for all preamblesequences. Thus, the state detection module 185 does not have to detectthe predetermined states of preamble sequences, and the modulo-2 summingmodule 186 may read the predetermined states of preamble sequencesdirectly from the control module 188 when performing cross-correlation.

The control module 188 estimates a preamble sequence index i from thecross-correlation values generated by the modulo-2 summing module 186 asfollows. The control module 188 selects the preamble sequence index forwhich the cross-correlation value with the differentially demodulatedsignal is largest. This may be mathematically expressed as follows.

$\hat{i} = {\underset{j}{\arg\;\max}\{ {\overset{\sim}{C}}_{j} \}}$The control module 188 determines that a preamble sequence is detectedif the magnitude of the largest cross-correlation value is greater thanor equal to a predetermined threshold. The predetermined threshold maybe based on the strength of the input signal.

Although the system 180 utilizes low-complexity cross-correlation byperforming XOR operations instead of actual correlation operations todetect a preamble sequence, the system 180 may reliably detect thepreamble sequence. That is, the system 180 may not mis-detect or fail todetect a preamble sequence. This is because of two reasons: First, thepilot sub-carriers for preamble sequences have higher SNRs than regulardata sub-carriers since the pilot sub-carriers have approximately 9 dBhigher energy than regular data sub-carriers. This helps indistinguishing a preamble symbol from a data symbol and in detecting thepreamble symbol, thereby reducing probability of mis-detection ordetection failure.

Second, the preamble sequences have high redundancy, which may help inincreasing the accuracy with which preamble sequences may be detecteddespite using XOR operations instead of actual correlation operations.Specifically, in 1024 FFT mode, less than 7 bits would be sufficient torepresent 114 preamble sequences (since 2⁷=128, which is more than 114).Additionally, each preamble sequence is 284-bits long wherein 7 bits areencoded to represent 284 symbols, thereby leaving many bits redundant.

The control module 188 determines which segment transmitted the detectedpreamble sequence implicitly when the control module 188 detects thepreamble sequence. This is because each preamble sequence is unique asidentified by a unique preamble sequence index number, and each segmenttransmits a unique preamble sequence using distinct sub-carriers. Whenthe control module 188 detects the preamble sequence by selecting thelargest cross-correlation value, the control module 188 implicitlyselects the segment having the largest channel gain (i.e., the bestsegment).

Occasionally, two or more preamble sequences may generatecross-correlation values that are larger than the rest and that areapproximately the same. For example, when a mobile station is adjacentto a cell boundary or a segment boundary, the mobile station may receiveinput signals including preamble sequences from adjacent base stations.

Thus the input signals received by the mobile station at cell or segmentboundaries may be a sum of up to three signals that may be transmittedby three different segments of three different base stations. This ismathematically expressed as follows.

${Y_{r}\lbrack k\rbrack} = {{\sum\limits_{s = 0}^{2}{{H_{r,s}\lbrack k\rbrack}{X_{i{(s)}}\lbrack k\rbrack}}} + {Z_{r}\lbrack k\rbrack}}$wherei(s)=preamble sequence index used for segment s,H_(r,s)[k]=preamble OFDMA symbol of segment s, andX_(i(s))[k]=channel gain corresponding to the segment s and receiveantenna r.

In that case, the modulo-2 summing module 186 may generatecross-correlation values that are similar and larger than the rest dueto presence of two or more preamble sequences in the received signals.Subsequently, the control module 188 may detect two or morecross-correlation values that are similar and that are larger than therest of the cross-correlation values.

Consequently, when using low-complexity cross-correlation, the bestsegment determined by the control module 188 may or may not in fact bethe best segment depending on the channel gain and noise. For example,when channel gain H_(r)[k] is very high, say 10, and noise Z_(r)[k] isvery low, say 0.1, the probability may be very high that the sign ofY_(r)[k] may be positive for a binary 0 and negative for a binary 1. Inthat case, the best segment determined by the control module 188 may infact be the best segment.

On the other hand, when H_(r)[k] is very low, say only 1, the signs ofY_(r)[k] may still be positive and negative for 0s and 1s, respectively.However, when the channel gain is very low and the noise level is high,the signs of Y_(r)[k] may not be positive and negative for 1s and 0s,respectively. That is, high noise levels may invert the sign of Y_(r)[k]when channel gain is very low. Sign inversions due to low channel gainand/or high noise may affect the ability of the control module 188 toaccurately select the segment since the low-complexity cross-correlationis based on signs of M[k] and D[k].

When two or more cross-correlation values are similar and larger thanthe rest, the control module 188 may select the correct segment in threeways. In one way, the control module 188 may randomly select one of thetwo or more larger cross-correlation values. Thus, the control module188 may select the segment that corresponds to the preamble sequencethat yielded the randomly selected larger cross-correlation value.

In another way, the control module 188 may select one of the two or morelarger cross-correlation values based on the strength of the inputsignals. That is, the control module 188 may select the largercross-correlation value that corresponds to the strongest input signal.This may be mathematically expressed as follows.

$\hat{s} = {\underset{s}{\arg{\;\;}\max}\{ {\sum\limits_{r = 1}^{R}{\sum\limits_{k \in P_{s}}{{Y_{r}\lbrack k\rbrack}}}} \}}$The control module 188 may accurately select the segment based on inputsignal strength when the noise level is approximately the same for allinput signals received from different segments.

In yet another way, the system 180 may include a correlation module 190that correlates the differentially demodulated input signals and thederived preamble sequences that generated the two or more larger andsimilar cross-correlation values. An example of such a system 181implemented in a PHY module 183 of a mobile station having at least tworeceive antennas is shown in FIG. 7B. Hereinafter, the differentiallydemodulated input signals and the derived preamble sequences thatgenerated the two or more larger and similar cross-correlation valueswill be called selected input signals and selected preamble sequences,respectively.

The correlation module 190 correlates the selected input signals withthe selected preamble sequences, generates correlation values, andoutputs the correlation values to the control module 188. Thecorrelation values are complex numbers, which have real and imaginaryparts. The imaginary parts of the correlation values represent noise inthe input signal.

When ∠(H[k]H*[k−3])≈0, i.e., when adjacent modulated sub-carriers havesimilar channel phase, the control module 188 disregards the imaginaryparts and selects a correlation value having a largest real part. Thecontrol module 188 selects the segment that corresponds to the preamblesequence that generated the correlation value having the largest realpart.

On the other hand, when the adjacent modulated sub-carriers have anunknown differential channel phase θ common to all k sub-carriers, thecontrol module 188 calculates the magnitude of the largest correlationvalue instead of selecting the real part of the largest correlationvalue. That is, the control module 188 does not disregard the imaginarypart of the largest correlation value. The control module 188 selectsthe segment that corresponds to the preamble sequence that generated thecorrelation value having the largest magnitude.

Referring now to FIGS. 8A-8B, a method 200 for detecting preamblesequences in a mobile station having at least two receive antennasbegins at step 202. In step 203, a correlation module 154 receives aninput signal from each receive antenna wherein each input signalincludes sub-carriers that are modulated using orthogonal frequencydivision multiplexing (OFDM). In step 204, a control module 156determines whether channels are almost frequency flat.

If true, the control module 156 determines in step 206 if an integercarrier frequency offset (CFO) is present in the input signal. If theinteger CFO is absent, the correlation module 154 correlates the inputsignal from each receive antenna with all preamble sequences in step 208and generates correlation values for each input signal. If the integerCFO is present, however, the correlation module 154 correlates thesignals shifted by the integer CFO with preamble sequences in step 210.

In step 211, the control module 156 adds correlation values thatcorrespond to the same preamble sequence for each input signal togenerate correlation sums. The control module 156 selects a largest ofthe correlation sums in step 212. The control module 156 checks if amagnitude of the largest correlation sum exceeds a predeterminedthreshold in step 214. If false, the control module 156 determines instep 216 that no preamble sequence is detected in the input signals, andthe method 200 ends in step 218.

If true, however, the control module 156 determines that a preamblesequence is detected in the input signals in step 220. Since eachpreamble sequence is unique and since each segment of each base stationtransmits using distinct sub-carriers, the control module 156 implicitlydetermines in step 224 which segment of a base station transmitted thedetected preamble sequence. The method 200 ends in step 218.

If, however, the result of step 204 is false, the control module 156divides the input signal received by each receive antenna into L bandsin step 226. The correlation module 154 correlates on a per-band basisand generates intra-band correlation values for each input signal instep 228. The control module 156 adds the intra-band correlation valuesand generates a magnitude of a sum of the intra-band correlation valuesto generate a band correlation value in step 230, thereby generating Lband correlation values for each preamble sequence per receive antenna.

The control module 156 adds the band correlation values for a preamblesequence to generate a correlation value for the preamble sequence instep 232, thereby generating i correlation values for i preamblesequences for each input signal in step 232. Steps starting at step 211are performed thereafter.

Referring now to FIG. 9A, a method 250 for detecting preamble sequencesin signals received by a MS via at least two receive antennas whenmoderately frequency selective channels have substantially the samechannel phase begins at step 252. A differential demodulation module 164receives an input signal from each receive antenna in step 254 whereineach input signal includes sub-carriers that are modulated usingorthogonal frequency division multiplexing (OFDM).

The differential demodulation module 164 differentially demodulates theinput signals and generates differentially demodulated signals in step256. A summing module 165 adds the differentially demodulated signalsand generates a combined differentially demodulated signal in step 257.

A control module 168 determines in step 258 if an integer carrierfrequency offset (CFO) is present in the input signals. If the integerCFO is absent, a correlation module 166 correlates the combineddifferentially demodulated signal with derived preamble sequences andgenerates correlation values in step 260. If the integer CFO is present,however, the correlation module 166 correlates in step 264 the derivedpreamble sequences with the combined differentially demodulated signalthat includes a shift caused by the integer CFO.

The control module 168 selects in step 266 a largest real part ofcorrelation values generated by the correlation module 166. The controlmodule 168 checks if the largest real part is greater than or equal to apredetermined threshold in step 268. If false, the control module 168determines in step 270 that no preamble sequence is detected in theinput signals, and the method 250 ends in step 272.

If true, however, the control module 168 determines that a preamblesequence is detected in the input signals in step 274. Since eachpreamble sequence is unique and since each segment of each base stationtransmits using distinct sub-carriers, the control module 168 implicitlydetermines in step 276 which segment of a base station transmitted thedetected preamble sequence. The method 250 ends in step 272.

Referring now to FIG. 9B, a method 350 for detecting preamble sequencesin signals received by a MS via at least two receive antennas whenmoderately frequency selective channels have substantially the samedifferential channel phase begins at step 352. A differentialdemodulation module 164 receives an input signal from each receiveantennas in step 354 wherein each input signal includes sub-carriersthat are modulated using orthogonal frequency division multiplexing(OFDM).

The differential demodulation module 164 differentially demodulates theinput signals and generates differentially demodulated signals in step356. A summing module 165 adds the differentially demodulated signalsand generates a combined differentially demodulated signal in step 357.

A control module 168 determines in step 358 if an integer carrierfrequency offset (CFO) is present in the input signals. If the integerCFO is absent, a correlation module 166 correlates the combineddifferentially demodulated signal with derived preamble sequences andgenerates correlation values in step 360. If the integer CFO is present,however, the correlation module 166 correlates in step 364 the derivedpreamble sequences with the combined differentially demodulated signalthat include the shift caused by the integer CFO.

The control module 168 selects in step 366 a largest correlation valuefrom the correlation values generated by the correlation module 166. Thecontrol module 168 checks if a magnitude of the largest correlationvalue is greater than or equal to a predetermined threshold in step 368.If false, the control module 168 determines in step 370 that no preamblesequence is detected in the input signals, and the method 350 ends instep 372.

If true, however, the control module 168 determines that a preamblesequence is detected in the input signals in step 374. Since eachpreamble sequence is unique and since each segment of each base stationtransmits using distinct sub-carriers, the control module 168 implicitlydetermines in step 376 which segment of a base station transmitted thedetected preamble sequence. The method 350 ends in step 372.

Referring now to FIG. 9C, a method 400 for detecting preamble sequencesin signals received by a MS via at least two receive antennas whenmoderately frequency selective channels have substantially the samechannel phase begins at step 402. A differential demodulation module 164receives an input signal from each receive antennas in step 404 whereineach input signal includes sub-carriers that are modulated usingorthogonal frequency division multiplexing (OFDM).

The differential demodulation module 164 differentially demodulates theinput signals and generates differentially demodulated signals in step405. A summing module 165 adds the differentially demodulated signalsand generates a combined differentially demodulated signal in step 406.A state detection module 185 detects states (i.e., signs) of symbols inthe combined differentially demodulated signal in step 407.

A control module 188 determines in step 408 if an integer carrierfrequency offset (CFO) is present in the input signal. If the integerCFO is absent, a modulo-2 summing module 186 cross-correlates (XORs) thestates of the symbols in the combined differentially demodulated signalwith predetermined sates of preamble sequences and generatescross-correlation values in step 410. If the integer CFO is present,however, the modulo-2 summing module 186 correlates in step 414 thepredetermined states of preamble sequences with the states of symbols inthe combined differentially demodulated signal that includes a shiftcaused by the integer CFO.

The control module 188 selects in step 416 a largest of thecross-correlation values generated by the modulo-2 summing module 186.The control module 188 checks if the largest cross-correlation value isgreater than or equal to a predetermined threshold in step 418. Iffalse, the control module 188 determines in step 420 that no preamblesequence is detected in the input signals, and the method 400 ends instep 422.

If true, however, the control module 188 checks if two or morecross-correlation values are similar and larger than the rest in step424. If false, the control module 188 determines that a preamblesequence is detected in the input signals in step 426. Since eachpreamble sequence is unique and since each segment of each base stationtransmits using distinct sub-carriers, the control module 168 implicitlydetermines in step 443 which segment of a base station transmitted thedetected preamble sequence. The method 400 ends in step 422.

If the result of step 424 is true, then in step 430, a correlationmodule 190 correlates the differentially demodulated signals and thederived preamble sequences that generated the two or more similar andlarge cross-correlation values. In step 432, the control module 188selects either the real part or the magnitude of the largest of thecorrelation values generated by the correlation module 190. The controlmodule 188 implicitly determines in step 443 which segment of a basestation transmitted the detected preamble sequence. The method 400 endsin step 422.

Although every third sub-carrier is modulated as described in thesystems and methods disclosed in this disclosure, skilled artisans canappreciate that the systems and methods disclosed herein may beimplemented by modulating every P^(th) sub-carrier, where P is aninteger greater than 1. Thus, if P=2, the systems and methods disclosedherein may be implemented by modulating every other (i.e., alternate)sub-carrier, etc.

Referring now to FIGS. 10A-10C, various exemplary implementationsincorporating the teachings of the present disclosure are shown.Referring now to FIG. 10A, the teachings of the disclosure may beimplemented in a WiMAX interface 452 of a vehicle 446. The vehicle 446may include a vehicle control system 447, a power supply 448, memory449, a storage device 450, the WiMAX interface 452, and a plurality ofassociated antennas 453. The vehicle control system 447 may be apowertrain control system, a body control system, an entertainmentcontrol system, an anti-lock braking system (ABS), a navigation system,a telematics system, a lane departure system, an adaptive cruise controlsystem, etc.

The vehicle control system 447 may communicate with one or more sensors454 and generate one or more output signals 456. The sensors 454 mayinclude temperature sensors, acceleration sensors, pressure sensors,rotational sensors, airflow sensors, etc. The output signals 456 maycontrol engine operating parameters, transmission operating parameters,suspension parameters, etc.

The power supply 448 provides power to the components of the vehicle446. The vehicle control system 447 may store data in memory 449 and/orthe storage device 450. Memory 449 may include random access memory(RAM) and/or nonvolatile memory such as flash memory, phase changememory, or multi-state memory, in which each memory cell has more thantwo states. The storage device 450 may include an optical storage drive,such as a DVD drive, and/or a hard disk drive (HDD). The vehicle controlsystem 447 may communicate externally using the WiMAX interface 452.

Referring now to FIG. 10B, the teachings of the disclosure can beimplemented in a WiMAX interface 468 of a cellular phone 458. Thecellular phone 458 includes a phone control module 460, a power supply462, memory 464, a storage device 466, and a cellular network interface467. The cellular phone 458 may include the WiMAX interface 468 and aplurality of associated antennas 469, a microphone 470, an audio output472 such as a speaker and/or output jack, a display 474, and a userinput device 476 such as a keypad and/or pointing device.

The phone control module 460 may receive input signals from the cellularnetwork interface 467, the WiMAX interface 468, the microphone 470,and/or the user input device 476. The phone control module 460 mayprocess signals, including encoding, decoding, filtering, and/orformatting, and generate output signals. The output signals may becommunicated to one or more of memory 464, the storage device 466, thecellular network interface 467, the WiMAX interface 468, and the audiooutput 472.

Memory 464 may include random access memory (RAM) and/or nonvolatilememory such as flash memory, phase change memory, or multi-state memory,in which each memory cell has more than two states. The storage device466 may include an optical storage drive, such as a DVD drive, and/or ahard disk drive (HDD). The power supply 462 provides power to thecomponents of the cellular phone 458.

Referring now to FIG. 10C, the teachings of the disclosure can beimplemented in a network interface 494 of a mobile device 489. Themobile device 489 may include a mobile device control module 490, apower supply 491, memory 492, a storage device 493, the networkinterface 494, and an external interface 499. The network interface 494includes a WiMAX interface and an antenna (not shown).

The mobile device control module 490 may receive input signals from thenetwork interface 494 and/or the external interface 499. The externalinterface 499 may include USB, infrared, and/or Ethernet. The inputsignals may include compressed audio and/or video, and may be compliantwith the MP3 format. Additionally, the mobile device control module 490may receive input from a user input 496 such as a keypad, touchpad, orindividual buttons. The mobile device control module 490 may processinput signals, including encoding, decoding, filtering, and/orformatting, and generate output signals.

The mobile device control module 490 may output audio signals to anaudio output 497 and video signals to a display 498. The audio output497 may include a speaker and/or an output jack. The display 498 maypresent a graphical user interface, which may include menus, icons, etc.The power supply 491 provides power to the components of the mobiledevice 489. Memory 492 may include random access memory (RAM) and/ornonvolatile memory such as flash memory, phase change memory, ormulti-state memory, in which each memory cell has more than two states.The storage device 493 may include an optical storage drive, such as aDVD drive, and/or a hard disk drive (HDD). The mobile device may includea personal digital assistant, a media player, a laptop computer, agaming console, or other mobile computing device.

Those skilled in the art can now appreciate from the foregoingdescription that the broad teachings of the disclosure can beimplemented in a variety of forms. Therefore, while this disclosureincludes particular examples, the true scope of the disclosure shouldnot be so limited since other modifications will become apparent to theskilled practitioner upon a study of the drawings, the specification andthe following claims.

1. A system comprising: a differential demodulation module configured togenerate differentially demodulated signals based on havingdifferentially demodulated received signals, and a first summing moduleconfigured to generate a combined signal by adding the differentiallydemodulated signals, wherein the combined signal includes a plurality ofsymbols; and a second summing module configured to generate a pluralityof sums for each of a plurality of derived preamble sequences, whereinthe derived preamble sequences are derived from preamble sequences,wherein each of the derived preamble sequences includes a plurality ofderived symbols, and wherein one of the plurality of sums generated forone of the derived preamble sequences is a sum of (i) a first portion ofone of the plurality of symbols of the combined signal and (ii) a secondportion of one of the derived symbols of the one of the derived preamblesequences, and generate cross-correlation values for the derivedpreamble sequences based on the plurality of sums, wherein one of thecross-correlation values generated for one of the derived preamblesequences is a sum of the plurality of sums generated for the one of thederived preamble sequences.
 2. The system of claim 1, wherein: the firstportion of the one of the plurality of symbols includes a polarity of areal portion of the one of the plurality of symbols; the second portionof the one of the derived symbols includes a reversed polarity of theone of the derived symbols; and the sum is a modulo-2 sum.
 3. The systemof claim 1, wherein: one of the derived symbols of one of the derivedpreamble sequences has a first binary value when a corresponding symboland a symbol adjacent to the corresponding symbol in a corresponding oneof the preamble sequences have opposite binary values, and the one ofthe derived symbols has a second binary value that is opposite to thefirst binary value when the corresponding symbol and the symbol adjacentto the corresponding symbol have the same binary value.
 4. The system ofclaim 1, further comprising a control module configured to: select alargest cross-correlation value from the cross-correlation values, anddetect one of the preamble sequences in the received signals in responseto the largest cross-correlation value being greater than or equal to apredetermined threshold, wherein the predetermined threshold is based ona signal strength of the received signals.
 5. The system of claim 4,wherein the control module is configured to identify, based on thedetected preamble sequence, a segment of a base station that transmittedthe received signals.
 6. The system of claim 1, further comprising: acorrelation module configured to generate correlation values, inresponse to two or more of the cross-correlation values being greaterthan or equal to a predetermined threshold, by correlating (i) thedifferentially demodulated signals and (ii) the derived preamblesequences that caused the two or more of the cross-correlation values tobe greater than or equal to the predetermined threshold, wherein thepredetermined threshold is based on a signal strength of the receivedsignals.
 7. The system of claim 6, further comprising a control moduleconfigured to: select one of the correlation values having a largestreal portion, detect one of the preamble sequences in the receivedsignals based on the largest real portion, and identify, based on thedetected preamble sequence, a segment of a base station that transmittedthe received signals.
 8. The system of claim 6, further comprising acontrol module configured to: select one of the correlation valueshaving a largest magnitude, detect one of the preamble sequences in thereceived signals based on the largest magnitude, and identify, based onthe detected preamble sequence, a segment of a base station thattransmitted the received signals.
 9. A method comprising: generatingdifferentially demodulated signals by differentially demodulatingreceived signals; generating a combined signal by adding thedifferentially demodulated signals, wherein the combined signal includesa plurality of symbols; generating a plurality of sums for each of aplurality of derived preamble sequences, wherein the derived preamblesequences are derived from preamble sequences, wherein each of thederived preamble sequences includes a plurality of derived symbols, andwherein one of the plurality of sums generated for one of the derivedpreamble sequences is a sum of (i) a first portion of one of theplurality of symbols of the combined signal and (ii) a second portion ofone of the derived symbols of the one of the derived preamble sequences;and generating cross-correlation values for the derived preamblesequences based on the plurality of sums, wherein one of thecross-correlation values generated for one of the derived preamblesequences is a sum of the plurality of sums generated for the one of thederived preamble sequences.
 10. The method of claim 9, wherein: thefirst portion of the one of the plurality of symbols includes a polarityof a real portion of the one of the plurality of symbols; the secondportion of the one of the derived symbols includes a reversed polarityof the one of the derived symbols; and the sum is a modulo-2 sum. 11.The method of claim 9, wherein: one of the derived symbols of one of thederived preamble sequences has a first binary value when a correspondingsymbol and a symbol adjacent to the corresponding symbol in acorresponding one of the preamble sequences have opposite binary values,and the one of the derived symbols has a second binary value that isopposite to the first binary value when the corresponding symbol and thesymbol adjacent to the corresponding symbol have the same binary value.12. The method of claim 9, further comprising: selecting a largestcross-correlation value from the cross-correlation values, and detectingone of the preamble sequences in the received signals in response to thelargest cross-correlation value being greater than or equal to apredetermined threshold, wherein the predetermined threshold is based ona signal strength of the received signals.
 13. The method of claim 12,further comprising identifying, based on the detected preamble sequence,a segment of a base station that transmitted the received signals. 14.The method of claim 9, further comprising: generating correlationvalues, in response to two or more of the cross-correlation values beinggreater than or equal to a predetermined threshold, by correlating (i)the differentially demodulated signals and (ii) the derived preamblesequences that caused the two or more of the cross-correlation values tobe greater than or equal to the predetermined threshold, wherein thepredetermined threshold is based on a signal strength of the receivedsignals.
 15. The method of claim 14, further comprising: selecting oneof the correlation values having a largest real portion, detecting oneof the preamble sequences in the received signals based on the largestreal portion, and identifying, based on the detected preamble sequence,a segment of a base station that transmitted the received signals. 16.The method of claim 14, further comprising: selecting one of thecorrelation values having a largest magnitude, detecting one of thepreamble sequences in the received signals based on the largestmagnitude, and identifying, based on the detected preamble sequence, asegment of a base station that transmitted the received signals.